1. Field of the Invention
The present invention relates to photo-reflectance characterization of semiconductor structures and, more particularly, to photo-reflectance beam spatial profiling techniques. The present invention provides methods and apparatuses to perform beam profiling of photo-reflectance light beams and to independently measure refractive and absorptive non-linearities occurring in photo-reflectance measurements.
2. Background of the Invention
High sensitivity measurement techniques are required for process control during the volume manufacture of electronic devices. One of the most useful techniques in this regard is an optical technique known as photo-reflectance, which may be used to rapidly, nondestructively and precisely characterize very small optical signatures related to the electronic properties of semiconductor nanostructures. Photo-reflectance techniques are routinely used to measure differential changes in reflectivity smaller than one part per million.
In conventional photo-reflectance, a pump laser beam is used to periodically modulate the carrier density in a semiconductor sample, and hence modulate one or more physical quantities (such as, for example, near surface electric fields), thereby inducing a periodic variation in the reflectivity of the sample, which is then recorded by use of a coincident probe light beam. In general, the photo-reflectance signal may be written:ΔR/R=αΔ∈1+βΔ∈2,  (1)wherein ΔR/R is the normalized change in reflectivity, α≡1/R×(∂R/∂∈1) and β≡1/R×(∂R/∂∈2) are the “Seraphin coefficients,” which contain filmstack information, and Δ∈1 and Δ∈2 are the pump induced changes in the real and imaginary parts of the complex dielectric function, respectively. [B. O. Seraphin and N. Bottka, “Field Effect of the Reflectance in Silicon,” Phys. Rev. Lett. 15, 104-107 (1965); J. C. Philips and B. O. Seraphin, “Optical-Field Effect on Thresholds, Saddle-Point Edges, and Saddle-Point Excitons,” Phys. Rev. Lett. 15, 107-110 (1965); B. O. Seraphin, “Optical Field Effect in Silicon,” Phys. Rev. 140, A 1716-1725 (1965); B. O. Seraphin and N. Bottka, “Band-Structure Analysis from Electro-Reflectance Studies,” Phys. Rev. 145, 628-636 (1966); D. Aspnes, “Modulation Spectroscopy,” in Handbook on Semiconductors, Vol. 2, edited by M. Balkanski, pp. 109 (North-Holland, Amsterdam, 1980) (“Aspnes 1980”); F. H. Pollak, “Modulation Spectroscopy of Semiconductors and Semiconductor Microstructures,” in Handbook on Semiconductors, Vol. 2, edited by M. Balkanski, pp. 527-635 (North-Holland, Amsterdam, 1994). (“Pollak 1994”)].
Δ∈1 and Δ∈2 contain all the optical information available concerning the response of the material to the external modulation of any physical parameter. For example, modulated changes in the electric field produce changes in the reflectance according to the relation:ΔR/R=1/R×(∂R/∂F)ΔF,  (2)wherein F is the electric field. Using Equations (1) and (2), Δ∈1 and Δ∈2 may be identified as:Δ∈i=(∂∈i/∂F)ΔF,  (3)which provides the relationship between the material optical response and the modulation of the external parameter, in this case the electric field.
The presence of an electric field is known to produce a redshift of semiconductor interband transitions. [L. V. Keldysh, “The Effect Of A Strong Electric Field On The Optical Properties Of Insulating Crystals,” L. V. Keldysh, Soviet Physics—JETP 34(7), 788-780 (1958)]. This electric field effect produces a sharp third-derivative signature in the electro-reflectance and/or photo-reflectance spectrum at the position of the semiconductor interband transition. [Aspnes 1980; Pollak 1994]. The photoreflectance signal arises from the electro-modulation effect for probe wavelengths nearby to semiconductor interband transitions. [Aspnes 1980].
Effective application of photo-reflectance to provide process control of semiconductor electronic properties in volume manufacturing is dependent on certain constraints, including (i) the ability to modulate the near-surface electrical field in the region of interest, (ii) the sensitivity of the probe to changes in the electric field, and (iii) the practical realization of process control criteria, such as high measurement speed, repeatability, spot size, etc.
To appreciate these constraints, it is instructive to consider an industry accepted process control application of photo-reflectance. Historically, ion implant monitoring in volume silicon IC manufacturing was accomplished with a photo-reflectance technique using a 488 nm wavelength laser pump beam in conjunction with a 633 nm laser probe. In such a process, a pump laser beam of several milliwatts is focused to a micron spot on a silicon wafer, producing an induced charge density on the order 1018/cm3. The presence of carriers modifies the silicon dielectric function through the addition of a Drude carrier plasma term and through a small temperature rise (approximately 1° C.).
This “modulated optical reflectivity” signal arises from distinct physical effects—the external modulation of temperature and carrier plasma density—and therefore may be generally modeled by: R/R=Δ(∂R/∂T)ΔT+(∂R/∂N)ΔN, wherein T is temperature, and N is carrier plasma density. [J. Opsal, and A. Rosencwaig, “Thermal and plasma wave depth profiling in silicon,” Appl. Phys. Lett. 47, 498 (1985) (“Opsal 1985”); A. Rosencwaig, et al., “Comment on ‘Spatially resolved defect mapping in semiconductors using laser-modulated thermoreflectance,’” Appl. Phys. Lett. 49, 301 (1986); Jon Opsal, et al., “Temporal behavior of modulated optical reflectance in silicon,” J. Appl. Phys. 61, 240 (1987) (“Opsal 1987”)]. Each term has a distinct dependence on wavelength, or dispersion. The plasma modulation contribution is generally modeled after the Drude effect and is proportional to the square of the probe wavelength. [Opsal 1985; Opsal 1987]. Thus, the Drude plasma dispersion effect is suppressed at shorter wavelengths and therefore measurement of Drude carrier modulation is preferred at longer wavelengths, such as, for example, in the near-IR. At 633 nm, only changes in the real part of the Si dielectric function are significant.
In such circumstance, the photo-reflectance signal then simplifies to: ΔR/RαΔ∈1. In a typical scenario, the Seraphin coefficient is roughly α≈4×10−2, and the change in the dielectric function due to the Drude carrier plasma is Δ∈1≈−3×10−3, producing a plasma contribution to the photo-reflectance signal of ΔR/R−1×10−4. As it turns out, near 600 nm, a thermal term of opposite sign nearly cancels the plasma contribution, resulting in observed signals on the order 1×10−5 or less. [Opsal 1985]. Notwithstanding this circumstance, this historical implementation of photo-reflectance has provided a basic “go/no go” implant process monitoring capability in IC manufacturing. However, due to the 633 nm wavelength being far from any significant optical features in silicon, the probe has no sensitivity to internal electric fields and/or interband transition energies. [Opsal 1985]. This fundamental problem severely limits the usefulness of thermo-modulation and carrier modulation measurement methods.
Ideally, the photo-reflectance apparatus is configured in a manner such that a given physical property may be determined in a straightforward fashion. For example, a photo-reflectance technique developed by the Applicant teaches the implementation photo-reflectance in a manner effective to characterize strain and active dopant in semiconductor manufacturing. [U.S. Pat. No. 7,391,507, issued to William W. Chism II on Jun. 24, 2008, entitled “Method of photo-reflectance characterization of strain and active dopant in semiconductor structures” (incorporated herein by reference)].
In that photo-reflectance technique, photo-reflectance probe wavelengths nearby strong optical absorptions in the semiconductor band structure are utilized such that the photo-reflectance signal arises from modulation of the surface electric field (electromodulation). In particular, this technique attains sensitivity to the active electronic properties of Si nanostructures by using a probe wavelength near the “E1” interband transition in Si, which occurs at a wavelength of approximately 375 nm. In the vicinity of such a transition, the induced changes in the dielectric function Δ∈1 and Δ∈2 may be written as the product of a free carrier energy and a third derivative of the semiconductor dielectric function: Δ∈=∂3(ω2∈)/∂ω3×UF, wherein UF is a free carrier energy, ω is the photon frequency (energy), and ∈ is the complex dielectric functions ∈≡∈1+i∈2.
Thus, one reason for selecting the wavelength of the probe beam at 375 nm for Si lies in the sharp derivative form for Δ∈1 and Δ∈2. The electro-modulation component then becomes:1/R×(∂R/∂F)ΔF=Re[(α−iβ)×∂3(ω2∈)/∂ω3)]×UF,  (4)wherein UF=e2h2F2/24 mω2, e is the electronic charge, h is Planck's constant, F is the electric field, and m is the carrier effective mass. This sharp derivative form is large only nearby strong optical absorptions in the semiconductor band structure, and may be used to measure the location of interband transitions with great precision. This is what allows the photo-reflectance technique to precisely measure strain in nanoscale strained silicon layers, for example, since the Si E1 transition energy undergoes a known shift under strain. Nearby to these strong optical absorptions, the amplitude of the photo-reflectance response also has excellent sensitivity to electric fields. The electric field of UF is the near surface electric field. This term is typically proportional to the surface carrier density, which may be understood from the (approximate) Poisson relation: N=∈oF2/2 eV wherein N is the carrier density, V is the built-in surface voltage, and ∈o is the permittivity of the material.
In the wavelength range of approximately 360-380 nm, the electric field modulation effect dominates the photo-reflectance response of silicon. The thermo-modulation and/or carrier modulation contributions to the photo-reflectance signal are typically below the detection limit of the photo-reflectance apparatus. Moreover, because the photo-reflectance signal is highly sensitive to the near surface electrical fields, it may be used to precisely measure activated dopant in Si transistor structures.
Because the photo-reflectance signal takes the form of a sum of contributions from the change in refraction and absorption (see Equation (1), above), it was not possible to independently determine the changes in nonlinear refraction and nonlinear absorption, i.e., what portion of the photo-reflectance signal arises from Δ∈1 or Δ∈2. Accordingly, there is a need for a method and apparatus for independently determining the refractive and absorptive changes induced in photo-modulated reflectance as well as thermo-elastic effects.
“Z-scan” techniques based on the principles of spatial beam distortion are known to provide simple means to measure spatial beam distortion due to nonlinear refraction and absorption of materials. [M. Sheik-Bahae, et al., “High-sensitivity, single beam n2 measurements,” Optics Lett. 14, 955 (1989); M. Sheik-Bahae, et al., “Sensitive Measurement of Optical Nonlinearities Using a Single Beam,” IEEE Journal of Quantum Electronics 26, 760 (1990); A. A. Said, et al., “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9, 405 (1992); E. W. Van Stryland and M. Sheik-Bahae, “Z-Scan Measurements of Optical Nonlinearities,” in Characterization Techniques and Tabulations for Organic Nonlinear Materials, M. G. Kuzyk and C. W. Dirk, Eds., pp. 655-692 (Marcel Dekker, 1998)].
Reflectance “z-scan” methods generally include performing sequence of reflected intensity measurements with a highly focused laser beam such that “self-lensing” occurs as the sample surface is passed through the focal region. The induced phase change (spatial distortion) of the reflected beam causes a differential intensity to be measured with an aperture fixtured in the far field of the probe beam. The “open aperture” reflection z-scan configuration is useful to measure nonlinear refraction in opaque semiconductors, whereas the “small aperture” reflection z-scan may be utilized to measure absorptive nonlinearities and/or thermo-elastic surface deformations. [D. V. Petrov, A. S. L. Gomes, and Cid B. de Araujo, “Reflection Z-scan technique for measurements of optical properties of surfaces,” Appl. Phys. Lett. 65, 1067-1069 (1994); D. V. Petrov, “Reflection Z-scan technique for the study of nonlinear refraction and absorption of a single interface and thin film,” J. Opt. Soc. Am. B 13, 1491-1498 (1996) (“Petrov 1996”); R. A. Ganeev and A. I. Ryasnyansky, “Reflection z-scan measurements of opaque semiconductor thin films,” Phys. Stat. Sol. A 202, 120-125 (2005); R. A. Ganeev, “Nonlinear refraction and nonlinear absorption of various media,” J. Opt. A: Pure Appl. Opt. 7, 717-733 (2005) (“Ganeev 2005”)]. Z-scan techniques have been used in both transmission and reflectance configurations to measure nonlinear optical coefficients.